Both will read that way sometimes to a modern audience, though Chaplin's definitely better in that department. However, a large set of Keaton's oeuvre treats of that not at all. Avoid The General and stuff with names like "The Pale Face" (gee, I wonder if that will be problematic?) and you'll mostly be fine.

On the other hand, Chaplin was apparently terrible to women off-screen, so... there's that.